Method for Evaluating a Material on a Remote Side of a Partition using Ultrasonic Measurements

ABSTRACT

Methods are disclosed for evaluating a material on a remote side of a partition separating first and second domains wherein flexural waves within the partition are received by spaced-apart ultrasonic receivers and processed to determine the velocity of the waves propagating into the second domain from a first receiver to a second receiver located more remote from the transmitter than the first receiver and whose separation from the first receiver is known. Comparison of a theoretical phase velocity with the measured phase velocity of the recorded waves allows determination as to whether the flexural wave is propagating through solid. This may be based on a measurable deviation between the two curves occurring at a critical frequency, which may be identified by a perturbation in a group velocity plot. Discrimination may also be based on the gradient of a straight line that best-fits the attention dispersion of the frequency spectrum.

FIELD OF THE INVENTION

The present invention relates to evaluating a material on one side of apartition using acoustic measurements.

PRIOR ART

Prior art references considered to be relevant as a background to theinvention are listed below and their contents are incorporated herein byreference. Acknowledgement of the references herein is not to beinferred as meaning that these are in any way relevant to thepatentability of the invention disclosed herein. Each reference isidentified by a number enclosed in square brackets and accordingly theprior art will be referred to throughout the specification by numbersenclosed in square brackets.

-   [1] Li, J. and J. L. Rose (2006): Natural beam focusing of    non-axisymmetric guided waves in large-diameter pipes. Ultrasonics    44(1): 35-45.-   [2] Viktorov, I. A: Rayleigh and Lamb waves: physical theory and    applications. New York, Plenum Press (1967).-   [3] Rose, J. L: Ultrasonic Waves in Solid Media (2000) 107(4):    1807-1808.-   [4] Nelson, H. M: A universal dispersion curve for flexural wave    propagation in plates and bars. Journal of Sound and Vibration    (1971), 18(1), 93-100.-   [5] Sirevaag, T. PhD thesis shortly to be submitted to Norwegian    University of Science and Technology (NTNU).-   [6] van Kuijk, R., S. Zeroug, B. Froelich, M. Allouche, S. Bose, D.    Miller, J.-L. Le Calvez, V. Schoepf and A. Pagnin: A Novel    Ultrasonic Cased-Hole Imager for Enhanced Cement Evaluation,    International Petroleum Technology Conference (2005).-   [7] Zeroug, S., Yang, J. & Bose, S. U.S. Pat. No. 9,534,487 Cement    acoustic properties from ultrasonic signal amplitude dispersions in    cased wells.-   [8] Velichko, A: Excitation and scattering of guided waves:    relationships between solutions for plates and pipes, J Acoust Soc    Am. 2009 June; 125(6):3623-31. doi: 10.1121/1.3117441.

BACKGROUND

Oil wells are created by drilling a hole into the earth with a drillingrig that rotates a drill string with a bit attached. After the hole isdrilled to a prescribed depth, sections of steel tubing known as casingare set in the hole (slightly smaller than the borehole). The smallspace between the formation and the casing is cemented in order toprevent oil and gas migrating up to the surface. During the drilling,completion and permanent closure of an oil well, it is a challenge toverify if the cement has been squeezed up the annulus and has bondedproperly to the casing. If no pressure test is planned, the primarymethod to validate that the annulus is impermeable, is to use ultrasonicborehole logging. To improve the identification of whether animpermeable solid is bonding onto the casing, efforts have been made toprovide solutions for using ultrasonic logging in the field.

US2006198243 discloses a method and apparatus for determining theintegrity of a cement bond log disposed in the annular space between acasing and a wellbore. The method and apparatus induce a Lamb wave inthe casing and into the wellbore. The Lamb wave attenuates upon passagethrough the cement bond. The integrity of the cement bond log can bedetermined by analysis and evaluation of the attenuation results.

U.S. Pat. No. 9,534,487 [7] uses a transmitter and a number of receiversto measure zero-order mode (A₀) antisymmetric flexural Lamb waveforms.These are processed to obtain the amplitude attenuation dispersion plotand phase dispersion plot as functions of frequency as means tocharacterize the physical state of a casing and annular fill outside thecasing. The flexural attenuation technique obtains information bytransmitting a pressure wave (T₁) with oblique incidence at the casingwall that excites a guided wave propagating upwards in the casing. Theguided wave leaks off energy as it propagates, and the leaked offpressure wavefront is measured at receivers positioned further up thewell. Since the flexural wave leaks energy as it propagates, the wave isconstantly attenuated as the distance increases.

U.S. Pat. No. 9,534,487 also notes that a perturbation in the ultrasonicpitch-catch measurements may appear under a certain condition. Further,perturbations of the estimated dispersion information across depth zonesor azimuthal ranges can be related to cement defects such ascontamination by mud, cracking, as well as the existence of channelsthat may permit hydraulic channeling. The cement wavespeeds are chosensuch that there is a discontinuity in the flexural wave attenuationdispersion curve. The estimated value, V_(o), around 2,600 m/s,corresponds to the bulk wavespeed of the cement in the annulus betweencasing and formation. Regardless of whether it is compressional or shearwavespeed, at around 2,600 m/s the value indicates the content of theannulus is made of a solid. The ultrasonic waveforms are processed toobtain (i) an amplitude attenuation dispersion plot of attenuation as afunction of frequency and (ii) a phase dispersion plot of phase velocityas a function of frequency. Barrier wave-speeds are determined byidentifying discontinuities within the amplitude attenuation dispersionplot, which are then related to the discontinuities to barrierwavespeeds using the phase dispersion plot.

U.S. Pat. No. 10,138,727 processes zero-order mode antisymmetric Lambflexural waveforms to identify barrier parameters as a function ofazimuth and depth along the borehole, wherein the waveforms comprise atleast two of sonic signals, ultrasonic pulse-echo signals, andultrasonic pitch-catch signals.

SUMMARY OF THE INVENTION

In accordance with the invention there are provided methods forevaluating a material on a remote side of a partition having thefeatures of the independent claims.

The present invention differs from known approaches such as disclosed in[7] in determining a theoretical phase velocity of the flexural wavepropagating through a domain on a side of the partition remote from thetransducers. Comparison of the theoretical phase velocity with themeasured phase velocity of the recorded waves allows determination as towhether the flexural wave is propagating through solid. A furtherfeature of the invention is that the perturbation is more easilymeasured when calculating and plotting the group velocity of theflexural wave (pulse) as a function of frequency. Thus, an embodiment ofthe present invention estimates the frequency where the perturbationoccurs in the group velocity plot and then uses an analytical solution,such as described in [4] Nelson, H. M. (1971) to find the velocity asthat frequency and relate this velocity to the velocity in the materialoutside the casing. In yet another embodiment, instead of looking for adiscontinuity in the attenuation dispersion plot, the inventionquantifies the frequency dependence of the attenuation over a predefinedinterval as will be discussed below.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to understand the invention and to see how it may be carriedout in practice, embodiments will now be described, by way ofnon-limiting example only, with reference to the accompanying drawings,in which:

FIG. 1 shows schematically a measuring method and system forcharacterizing the physical state of a partition installed in aborehole;

FIG. 2 shows schematically the orientation of the transducer withrespect to the partition;

FIG. 3 shows graphically idealized waveforms from ultrasonic pitch-catchmeasurements with the transducer directed to the partition at an angleof incidence to the normal of approximately 30°;

FIGS. 4a and 4b are graphical representations showing the flexural pulsewhen the annulus is filled with a liquid or solid, respectively;

FIGS. 5a and 5b are graphical representations showing respectively thefrequency spectrum of the flexural pulse and the accompanied phasevelocity between the spectra;

FIGS. 6a and 6b are graphical representations showing respectively thephase velocity and group velocity in the frequency domain highlightingthe perturbation from the group velocity according to the invention;

FIG. 7 is a generic flowchart showing the principal processingoperations to estimate the P-wave velocity of the annulus material fromthe flexural wave excited in the casing;

FIGS. 8a and 8b are graphical representations showing respectively thefrequency spectrum of the flexural pulse received at two spaced apartreceivers and the subsequent attenuation dispersion from propagating inthe casing the distance between the receivers;

FIG. 9 is a generic flowchart showing the principal analysis methodaccording to the invention; and

FIG. 10 is a generic flowchart showing the principal processingoperations to estimate the linear regression coefficient between theflexural waves excited in the casing.

DETAILED DESCRIPTION OF EMBODIMENTS

FIG. 1 shows schematically a measuring method and system according to anembodiment of the invention for characterizing the physical state of apartition installed in a borehole. The partition is constituted by thewall of a pipe known as a “casing” that is installed in a borehole, thusseparating a first domain inside the casing from a second domain outsidethe casing. The casing is surrounded by solid geological formation,which in the case of an oil or gas well is typically the sea bed. Thecasing usually comprises multiple sections of progressively narrowerbore the deeper they are inserted into the geological formation. Afterinstallation of each section of casing, it is cemented inside theborehole so as to form a secure rigid enclosure around the casing, whichserves as a conduit for accommodating the drill and releasing the oil orgas through perforations made in the portion of the casing which passesthrough the production zone, to provide a path for the oil to flow fromthe surrounding rock into the production tubing. Thus, with reference toFIG. 1 it is possible to define four domains as follows:

-   -   Domain 1 is the hollow space inside the casing;    -   Domain 2 is the annular space between the outer wall of the        casing and the formation. If there is no annular space, i.e. the        formation is bonded onto the casing, Domain 2 will vanish; and    -   Domain 3 is the wall, which constitutes a partition between the        formation and the first domain. In an oil well the partition        refers to a casing which is a larger pipe that is assembled and        inserted into the recently drilled section of the borehole;    -   Domain 4 is the geological formation.

We will refer to these four domains as first, second, third and fourthdomains, respectively.

At least one transmitter T₁ is positioned inside the casing, where thetransmitted signal propagates and hits the wall of the casing at anoblique incidence. The transmitted signal excites a guided wave insidethe wall of the casing formed of a known material and having a knownthickness.

From theory, a transducer positioned at an angle inside a liquid-filledpipe can excite guided waves that are similar to Lamb waves. Thediameter, d_(c), and the thickness, t_(c), of the cylindrical pipedetermine the deviation between the guided waves and the Lamb waves. Ifthe ratio d_(c)/t_(c) is above 10, which is typically the case in thefield, the difference is negligible [1]. The similarity also depends onthe frequency, but if the wavelength of the guided wave is much lessthan the pipe circumference and d_(c)/t_(c) is greater than 10, theeffect of the curvature becomes insignificant [8].

The well geometry can be understood in two dimensional spatialcoordinates, where the length of the partition is the axial directionand the azimuthal direction is simplified as only one direction.Further, in the frequency regime of interest, the two zero-order modesdominate the propagating wave in the partition. The zero-order symmetricmode (S₀) referred to as the extensional wave, has an ellipticalparticle displacement that is mainly parallel to the casing, i.e. in theaxial direction. The displacement of the zero-order antisymmetric mode(A₀), has an elliptical particle-motion mainly perpendicular to thepartition, i.e. a ‘bending’ or ‘flexural’ motion. Thus, the particlemotion in the casing is elliptical, with the vertex pointing in thedirection of the surrounding material, resulting in waves being emittedfrom each side of the casing, enabling Domain 2 to be investigated. Theexcitation of A₀ at the pipe/plate requires an oblique incidence anglearound 30° if Domain 1 is filled with water and Domain 3 is made ofsteel. This is illustrated in FIG. 2.

The system also requires at least two receivers, as seen in FIG. 1, asR₁ and R₂, both of which are located in Domain 1 and oriented in mirrorsymmetry to the transducer relative to a line normal to the outersurface of the casing at an angle of reflection that is equal to theincidence angle of the transducer. The flexural wave leaks off energy asit propagates, and the leaked off pressure wavefront is measured atreceivers positioned further up the well. Since the flexural wave leaksenergy as it propagates, the wave is being constantly attenuated as thedistance increases. The materials on both sides of the casing i.e. inDomains 1 and 2 affect the attenuation. Assuming the material insideDomain 1 is known, measuring the attenuation from one receiver to thenext provides information about the acoustic properties of the materialconstituting the annular space (Domain 2).

FIG. 3 shows graphically expected, idealized waveforms from flexurallogging in the field and illustrates the effect of a liquid filledannulus (Domain 2), where the first waveform is from R₁ and the secondwaveform is from R₂, as shown in FIG. 1. The first distinct pulse is thearrival of the emitted wavefront from the flexural wave (A₀). In thesecond waveform one can see the pulse has been attenuated, and the lossbetween the receivers gives an indication of what type of material is incontact with the casing. The second amplitude seen in the waveforms is aresult of the wavefront being reflected back at the interface betweenDomains 2 and 4. This pulse is often referred to as the third interfaceecho (TIE), where the first interface echo is between Domains 1 and 3,and the second interface echo is between Domains 2 and 3.

As the flexural wave propagates along the casing, waves are constantlybeing leaked off, and the waves being reflected at the third interfacegenerate a secondary zero-order flexural wave A₀ in the casing, markedas TIE in FIG. 3. Successive waves reflected at the third interfacecombine to produce a strong cumulative amplitude, and therefore, themeasured amplitude of the TIE can be larger for the second waveform thanfor the first as is shown in FIG. 3. The third amplitude is the directwave (D₁), or liquid borne waves, thus travelling slower than the otherpulses. This is seen in the figure, where the time difference betweenthe arrivals of the direct wave increases compared to the leaked offwavefront.

For the flexural wave to radiate longitudinal or pressure waves,commonly referred to as P-waves into the surroundings, the P-wavevelocity of the annulus material (v_(p,a)) needs to be lower than thedispersive phase velocity of the flexural wave (v_(A,φ)), as describedin [6]. If Domain 2 is a solid, the evaluation tends to be slightly morecomplex. v_(p,a) for a solid often overlaps or is higher than thedispersive v_(A,φ) (while this can also happen with a fluid, it is lesscommon). This will cause the radiation into the solid material to reducedrastically, and the velocity at which the two velocities are equal isreferred to as the critical velocity.

FIGS. 4a and 4b show graphically the flexural pulse when the annulus isfilled with a fluid or solid, respectively. The waveforms are field datafrom an oil well at the Utsira High area in the North Sea using acommercial tool optimized for ultrasonic borehole logging. The waveformswhere domain 2 is filled with a fluid is picked from a section way abovethe casing shoe. The casing shoe is the terminology used to indicate thebottom of the casing, and the field data presented are from a sectionmore than 400 meters above, so it is nearly physically impossible thatcement has been squeezed up that far. Therefore, the annulus is almostcertainly filled with a combination of the drilling mud used to drillout that section and the formation fluid in the pores. The waveformswhere domain 2 is filled with a solid is picked just above the casingshoe. The cement used in this oil well was foam cement, a cement typemixed with nitrogen that makes it light and results in a velocitybetween 2300-2700 m/s.

It is seen that the nicely preserved flexural pulse seen in FIG. 4abecomes partially obliterated as shown in FIG. 4b when a solid materialis in contact with the casing. As described in [5] and [7], themodification of the pulse is believed to happen during the transitionfrom a leaky-Lamb wave (v_(p,a)<v_(A) ₀ _(,φ)) to an evanescent wave(v_(p,a)>v_(A) _(0,φ) ). Snell's law estimates the refraction angle fora plane wave passing through a boundary between two different isotropicmedia. If the velocity of the propagating wave is below the velocity inthe surrounding medium, the outgoing angle can be greater than 90°depending on the angle of incidence. In this case, the plane wave isreflected and no energy is transmitted into the medium outside. It wouldthus appear that since the flexural wave has an ellipticalparticle-motion that is mainly perpendicular to the plane, the angle ofincidence at the interface will vary. Evanescent waves are formed whensinusoidal waves are leaked off a plate at a greater angle than thecritical angle, which would imply that the radiation at the interface isreduced. The wave that is leaked off into the annulus material is aP-wave, while the evanescent wave decays exponentially with the distancefrom the interface between the casing and the annulus material.

The transition causes the modification of the pulse. It is believed thata P-wave is excited in the annulus material and propagates parallel withthe casing with almost the same velocity as v_(A) ₀ _(,φ). The P-wavewill leak off energy into the casing, creating a second mode that hasits energy at the frequency where the dispersive v_(A) ₀ _(,φ)≈v_(P,a).The two modes will arrive at the receivers almost at the same time;hence the pulse seems to be smeared out. Furthermore, since thedeviation occurs where the P-wave velocity intersects the phasevelocity, processing in the frequency domain can be used to estimatev_(a,P).

By picking the pulse that originated from A₀ in the two receivers'waveforms (see FIG. 3) and performing a Fourier transform, one cananalyze the pulse in the frequency domain as seen in FIG. 5. Thefrequency spectra in FIG. 5a are for the liquid from FIG. 4 and thefrequency spectra in FIG. 5b are for the solid. One can see the tworeceivers R₁ and R₂ provide similar measurements but with differentsignal strengths.

Since v_(A,φ) is dispersive, the intersection with v_(p,a), can happenover a wider range of frequencies, but the effect is detectable only ifsufficiently amount of energy lies in the frequency spectrum (S_(w,n))where the P-wave and phase velocity overlap. The notation w is thewaveform, and n is a number indicating which receiver/distance. This isdemonstrated in FIGS. 5a and 5b , where the logarithmic, normalizedfrequency spectra of the flexural wave measured at R₁ and R₂ arerepresented by the solid and dashed curves respectively. The frequencyspectra in FIGS. 5a and 5b are from the same field data as presented inFIGS. 4a and 4b , respectively. The data demonstrates that the energy inthe flexural wave lies within a certain bandwidth. The horizontal axisis the frequency (f) multiplied by the casing thickness (d), which makesit easy to compare the different scales if the ratio f·d remainsconstant [3].

The chain-dotted black curve in FIG. 5a is an analytical solution asdescribed by Nelson [4], to calculate the dispersion curve for theflexural wave in casing material using the same plate Poisson's ratio,plate shear velocity, plate thickness and target frequency as in themeasured data. The vertical axis to the right shows the phase velocityof the flexural wave. For the sake of clarification, it should be notedthat FIGS. 5a and 5b each show two separate curves on a common abscissabut against different ordinates. Thus, the calculated wave velocitymeasured in units of m/s is plotted against the right-hand verticalaxis, while the measured phase velocity amplitude measured in units ofdB is plotted against the left-hand vertical axis.

The same type of plot was generated in FIG. 5b for a synthetic lightsolid, but here the phase velocity is also computed from the measureddata to compare to the analytical solution. By selecting the pulses thatoriginate from the flexural wave in the two receivers' waveforms,performing Fourier transforms, and measuring the phase angle in theinterval for each element of the complex signal in the frequency domain,one can find the phase shift Δφ between the pulses. The phase shiftbetween the pulses can also be expressed as:

Δφ=ω(t ₁ −z ₁ /v _(A) ₀ _(,φ))−ω(t ₂ −z ₂ /v _(A) ₀ _(,φ))  (1)

where ω is the angular frequency, t_(j) is the time of the selection ofthe first and second waveform, z_(j) gives the positions of thereceivers, and v_(A) ₀ _(,φ) is the flexural phase velocity presentedearlier. Since Δφ is already calculated from the arrival time, one canrearrange Eq. (1) and solve it to find v_(A) ₀ _(,φ).

As is seen from FIG. 5b there is an anomaly in the measurements at about175 kHz·cm, which is shown more clearly in FIG. 6a over a narrow rangeof wavespeed at enlarged scale. It is seen that for the specific foamcement in contact with the casing for which these results were derived,up to this critical frequency, denoted as f_(lim), the analytical curvefollows almost exactly the estimated phase velocity. However, at f_(lim)there is a slight deviation between the two curves, which then remainsubstantially parallel. It is known from [7] that a perturbation occurswhen the flexural phase velocity overlaps the P-wave velocity of theannulus material. The inventors have found surprisingly that, thevelocity at f_(lim) in the analytical solution can be related to thevelocity in Domain 2. The P-wave velocity in Domain 2 can be found byreading off the velocity of v_(A) ₀ _(,φ) at f_(lim). The wave velocitythrough a material is characteristic, and thus a good indication of thetype of material present at the opposite side of the casing wall.

It should be noted that the deviation providing the critical frequencycan only be found within the frequency range where the signal strengthis sufficient. This range is typically between 2000 m/s to 2900 m/s. So,detecting a deviation is indicative of the material being a solid. If nodeviation is observed, we cannot say if it is a solid or liquid, justthat the velocity of the material behind the casing is not between 2000m/s-2900 m/s.

The exact form of deviation may vary for different solid materials.Thus, for some materials the two curves may not follow each other priorto the critical frequency. Likewise, there may be materials where thedeviation is not sufficiently defined in the phase velocity plot toallow direct determination of the critical frequency. However, for thosephase velocity plots where it is possible to determine the criticalfrequency directly, the corresponding phase velocity at the criticalfrequency f_(lim) is compared to a predetermined threshold to determineif the space contains a liquid or a solid.

Alternatively, the invention provides a complementary technique todetermining the critical frequency f_(lim) at which a deviation occurs,which obviates the need to determine the critical frequency directlyfrom the phase velocity plot. To this end, it has been found that theperturbation is far more pronounced when the group velocity is plottedagainst frequency as will now be described.

The analytical solution and v_(A) ₀ _(,φ) seen in FIG. 5b are presentedin FIG. 6a together with the group velocity of the flexural wave(v_(A,g)) in FIG. 6b . In general, for the phase velocity v_(φ)=ω/k andthe group velocity v_(g)=dω/dk, estimation of the group velocityinvolves taking the derivative of the measured phase velocity. Becausethe deviation in the phase velocity in FIG. 6a is small, it is difficultto use the phase dispersion curves to detect f_(lim). Instead, a goodpractice would be to find f_(lim) in v_(A,g) and then estimate thevelocity at this frequency from the analytical solution to the phasevelocity. The group velocity dispersion curve shown in FIG. 6b shows aclear perturbation at around 175 kHz·cm, so for this synthetic dataf_(lim)=175 kHz·cm, whereby v_(P,a)=2600 m/s.

FIG. 7 is a generic flowchart that describes the processing to estimatethe P-wave velocity of the annulus material from the flexural waveexcited in the casing. The flowchart starts with the input of theflexural wave and knowledge of the pipe/plate and the center frequencyof the transmitted pulse. The final output is a velocity estimate ofacoustic waves propagating through domain 2.

Analyzing the Frequency Dependency of the Attenuation Dispersion

The system including at least two receivers may, however, also be usedto compute the attenuation dispersion of the flexural wave. From thefrequency spectrum measured at each receiver and shown in FIG. 8a , onecan estimate the attenuation at different frequencies. This attenuationcan be calculated by dividing the spectrum S_(w,n) by the spectrum atthe first receiver S_(w,1), performing a decibel conversion on thequotient, and then dividing this quotient by the distance between thereceivers:

$\begin{matrix}{\alpha_{(f)} = \frac{{- 2}0\log_{10}\left\{ \left| \frac{S_{w,n}}{S_{w,1}} \right| \right\}}{z_{n} - z_{1}}} & (2)\end{matrix}$

where α_((f)) is the attenuation in frequency domain. In FIG. 8b , theattenuation is plotted against the frequency. Outside the area coveredby the double arrow is where the signal level is low and likelydominated by noise. For fluids as the annulus material, the attenuationis quite constant. This behavior appears to hold for most fluids, whilethe attenuation tends to increase with increasing frequency for bondedsolids. The data presented is laboratory data with epoxy with 5%tungsten mixed in. The laboratory setup and measurements on epoxy ispresented by the inventor in a PhD thesis [5], which will be submittedshortly after filing the present application. It is noted that while thePhD thesis supplements what is described herein and provides moredetailed theoretical understanding, an understanding of the theory isnot essential to carrying out the invention, whose implementation isfully described herein without the need for further description and notall of whose features are related to in the PhD thesis.

The attenuation dispersion curve presented in FIG. 8b can be quantifiedby using least squares to estimate a linear fitted line (L_(a) _((f)) )to the behavior over the frequency:

L _(a) _((f)=a) _((f),0) +a _((f),1) C+a _((f),2) C ²+  (3)

where C=f·d and L_(a) _((f)) is expressed in dB/cm. a_((f)) is thelinear regression coefficient in dB/kHz, which is plotted in FIG. 9.Specifically, the ordinate in FIG. 9 shows the linear regressioncoefficient for various different solids and fluids, their values beingdenoted by the symbols ‘o’ and ‘+’, respectively. It is seen that solidshave a tendency to increase the attenuation when the frequency isincreasing. In effect, if we ignore the terms in C² and higher powers,which are negligible, this computes a straight line having gradienta_((f),1) that best-fits the attenuation dispersion curve. If thegradient is close to zero, this means that the attenuation is constantand the material behind the partition in Domain 2 is a fluid. If thegradient is greater than zero by a predetermined threshold e.g. 2·10⁻³db/kHz, this is indicative of the material being a solid.

It is not fully understood how the coupling of shear waves for solidsaffect the attenuation behavior in the frequency domain. We believe itis a combination of a P-wave velocity approaching a threshold value(1,800 m/s) and the coupling of shear waves, although reduction of theinvention to practice does not require a theoretical understanding ofthe actual mechanism. Nevertheless, a solid material with a P-wavevelocity below 1,800 m/s deep in the ground is uncommon. The oppositestatement can be made about fluids: it is very rare that a fluid has aP-wave velocity above 1,800 m/s deep in the ground as evidenced by thesimple fact that fluids tends to be more mixed with particles whichmakes them more dense which results in a reduced velocity. If the P-wavevelocity for a fluid is in the range of 2,100-2,800 m/s, we believe thisevent would increase a_((f)). Therefore this effect is not necessarilyrestricted to a solid, but rather the P-wave velocity of the annulusmaterial.

FIG. 10 shows a generic flowchart to describe the processing to estimatea_((f)) between the flexural waves excited in the casing. The flowchartstarts with the input of the flexural wave and knowledge of the distancebetween the receivers. The final output is parameter to quantify thefrequency dependence of the attenuation.

It should be noted that modifications may be made to both the method andsystem as described without departing from the scope of the invention asclaimed in the appended claims. In particular, it is noted that whilethe invention has been described with particular reference to evaluatinga material on the outside of a pipe or casing buried in the ground, theinvention may find more general application for discriminating betweentwo different materials on opposite sides of a partition. This may beuseful for evaluating whether liquid is present in a pipe used totransport liquid, thus allowing a blockage in the pipe to be detected.More generally, the partition does not need to be constituted by thewall of a cylindrical casing or pipe and can be any sheet materialhaving disparate materials on opposing surfaces thereof.

The invention has been described primarily with regard to a methodbecause the hardware is known per se. When used to monitor oil wells,the transmitter and receivers must be inserted into a hollow casing sunkin the ground that is possibly hundreds of meters deep. Since thedistances between adjacent receivers must be known, the transducers areinstalled into an elongated unit that is then lowered into the casing.This also allows the transducers to be tilted at known angles ofincidence and reflection although more advanced transducers areavailable where the wave angle can be adjusted electronically. However,when applied to other situations where the transducers are moreaccessible, they may be spaced apart discretely at known intervals.

It should also be noted that features that are described with referenceto one or more embodiments are described by way of example rather thanby way of limitation to those embodiments. Thus, unless stated otherwiseor unless particular combinations are clearly inadmissible, optionalfeatures that are described with reference to only some embodiments areassumed to be likewise applicable to all other embodiments also.

It will also be understood that the processing may be performed by asuitably programmed computer. Likewise, the invention contemplates acomputer program being readable by a computer for executing the methodof the invention. The invention further contemplates a machine-readablememory tangibly embodying a program of instructions executable by themachine for performing the method of the invention.

1. A method for evaluating a material on a remote side of a partitionseparating a first domain from a second domain, the method comprising:disposing at least one ultrasonic transmitter and a plurality ofultrasonic receivers in longitudinally spaced-apart relationship along afirst side of the partition in the first domain; activating the at leastone ultrasonic transmitter to form ultrasonic waveforms that comprisepropagated quasi leaky-Lamb waves constituting flexural waves havingsymmetrical and antisymmetric zero-order modes within the partition,wherein the spaced-apart receivers record the ultrasonic waveforms;processing the recorded ultrasonic waveforms to determine the phasevelocity of the waves propagating through the second domain on thesecond side of the partition from a first receiver to a second receiverthat is located more remote from the transmit-ter than the firstreceiver and whose separation from the first receiver is known;computing a theoretical phase velocity of the flexural wave propagatingthrough the second domain; and establishing that the second domaincontains a solid if the measured phase velocity deviates from thetheoretical phase velocity by an amount that is not accountable by noisealone.
 2. The method of claim 1, wherein establishing that the seconddomain contains a solid comprises: processing the ultrasonic waveformsto calculate the group velocity; identifying a perturbation in the groupvelocity plotted in the frequency domain and identifying a criticalfrequency f_(lim) at which the perturbation occurs; comparing the phasevelocity at the critical frequency f_(lim) to a predetermined thresholdto determine if the space contains a liquid or a solid.
 3. The method ofclaim 2, wherein calculating the group velocity includes (i) obtainingthe frequency spectrum of the isolated zero-order mode referred to asthe flexural pulse; (ii) estimating from the frequency spectrum thephase angle between the waveforms; and (iii) calculating the groupvelocity from the phase angle.
 4. The method of claim 3, wherein thephase angle is estimated from a portion of the frequency spectrum wherethe amplitude of the wavespeed exceeds a predetermined minimal signalstrength that eliminates the effect of noise.
 5. The method of claim 2,wherein identifying a perturbation in the flexural group velocitycomprises evaluation within a frequency range where the amplitude of thewavespeed exceeds a predetermined minimal signal strength thateliminates the effect of noise.
 6. The method of claim 2, whereinidentifying a perturbation in the group velocity comprises (i) computinga group velocity dispersion curve, and (ii) identifying a perturbationexceeding a predefined magnitude of deviation from the group velocitydispersion curve.
 7. The method of claim 1, wherein establishing thatthe space contains a solid comprises: identifying a deviation in themeasured phase velocity plotted in the frequency domain and identifyinga critical frequency f_(lim) at which the deviation occurs; determiningthe computed phase velocity at the critical frequency; and comparing thevelocity to a predetermined threshold to determine if the space containsa liquid or a solid.
 8. The method of claim 1, wherein the partitioncomprises a casing and an annular fill installed in a boreholetraversing a formation.
 9. The method of claim 1, wherein eachtransmitter and receiver is directed toward the partition at an angle ofincidence close to 30°.
 10. A computer program product comprising anon-transient computer readable medium storing program codeinstructions, which when executed on at least one processor thatreceives as input data representative of the recorded ultrasonicwaveforms from a pair of spaced apart receivers, carries out theprocessing and computing operations of claim
 1. 11. A method forevaluating materials on opposite first and second sides of a partitionseparating a first medium from a second medium, the method comprising:disposing at least one ultrasonic transmitter and a plurality ofultrasonic receivers in longitudinally spaced-apart relationship along afirst side of the partition in the first medium; activating the at leastone ultrasonic transmitter to form ultrasonic waveforms that comprisepropagated quasi leaky-Lamb waves constituting flexural waves havingsymmetrical and antisymmetric zero-order modes within the partition,wherein the spaced-apart receivers record the ultrasonic waveforms;processing the ultrasonic waveforms to (i) obtain a frequency spectrumof the isolated A₀ mode referred to as the flexural pulse; and (ii)compute an attenuation dispersion curve as a function of frequency;establishing whether the second domain contains a solid or a liquidbased on the gradient of a computed straight line that best-fits theattenuation dispersion curve within a predefined frequency range wherethe pulse has a signal strength that is above a minimal threshold. 12.The method of claim 11, wherein the minimal threshold is in the order of−20 dB.
 13. The method of claim 11, wherein establishing whether thesecond domain contains a solid or a liquid comprises: calculatingattenuation as a function of frequency within said predefined frequencyrange; estimating the linear regression coefficient from the attenuationdispersion curve using the least squares method; and using the linearregression coefficient to distinguish if the material in the seconddomain is a liquid or solid.
 14. The method of claim 13, whereinattenuation is calculated according to:$\alpha_{(f)} = \frac{{- 2}0\log_{10}\left\{ \left| \frac{S_{w,n}}{S_{w,1}} \right| \right\}}{z_{n} - z_{1}}$where: (S_(w,n)) is the frequency spectrum of the flexural pulse at then^(th) receiver; (S_(w,1)) is the frequency spectrum of the flexuralpulse at the first receiver; Z_(n)−Z₁ the distance between thereceivers.
 15. The method of claim 11, wherein the partition comprises acasing and an annular fill installed in a borehole traversing aformation.
 16. The method of claim 11, wherein each transmitter andreceiver is directed toward the partition at an angle of incidence closeto 30°.
 17. A computer program product comprising a non-transientcomputer readable medium storing program code instructions, which whenexecuted on at least one processor that receives as input datarepresentative of the recorded ultrasonic waveforms from a pair ofspaced apart receivers, carries out the processing and computingoperations of claim 11.